Select a value for b such that a triangle with A = 59° and a = 14 has only one solution.
A)b = 16
B)b = 17
C)b = 11
D)b = 15
E)b = 24

Question

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution. ​
A)b = 16
B)b = 17
C)b = 11
D)b = 15
E)b = 24

Quizplus · Accepted Answer

To have only one solution for the triangle, we need to make sure that the sine of the angle opposite to the given side is less than 1. This is because the sine function has a maximum value of 1. Using the sine law, we have:

b/sin(B) = a/sin(A)

Substituting the given values, we get:

b/sin(B) = 14/sin(59°)

To make sure there is only one solution, we need to make sure that sin(B) is less than or equal to 1. This means we need to choose a value of b such that:

b ≤ 14/sin(59°) ≈ 16.57

The only choice that satisfies this condition is C: b = 11.

Select a Value for B Such That a Triangle with a =